Each county in the district, organized under section 2151.65 of the Revised Code, shall be entitled to one trustee, and in districts composed of but two counties, each county shall be entitled to not less than two trustees. In districts composed of more than four counties, the number of trustees shall be sufficiently increased so that there shall always be an uneven number of trustees constituting such board. The county in which a district school, forestry camp, or other facility created under section 2151.65 of the Revised Code is located shall have not less than two trustees, who, in the interim period between the regular meetings of the board of trustees, shall act as an executive committee in the discharge of all business pertaining to the school, forestry camp, or other facility.